Wave Propagation in High-Contrast Media: Periodic and Beyond

Abstract

This work is concerned with the classical wave equation with a high-contrast coefficient in the spatial derivative operator. We first treat the periodic case, where we derive a new limit in the one-dimensional case. The behavior is illustrated numerically and contrasted to the higher-dimensional case. For general unstructured high-contrast coefficients, we present the Localized Orthogonal Decomposition and show a priori error estimates in suitably weighted norms. Numerical experiments illustrate the convergence rates in various settings.